The Federal Reserve appears to be ready to increase interest rates sooner than many economists were expecting, said Alan Krueger, former chairman of President Barack Obama's Council of Economic Advisers. But he insisted on CNBC Wednesday that the central bank is not yet behind the curve based on recent economic and jobs data.

Krueger dropped a bomb into the monetary policy debate, with the release of a controversial paper back in March, which asserted that the long-term unemployed are likely lost to the labor force. His theory is that the supply of available workers may be smaller than it appears, and wage pressures are likely to develop more quickly.

Jeff Rosenberg, chief investment strategist for fixed income at BlackRock, pointed out that Krueger's work "is critical to the debate that we're having in the markets."

But unlike Krueger, Rosenberg told CNBC Wednesday that he believes the Fed is "behind the curve" on interest rates are relative to the progress of the economic recovery, and markets are on edge about it.

"I have been following the long-term unemployed for a long time," Krueger said in a "Squawk Box" interview. "What I found is the longer they're unemployed, the more discouraged they become." He added, "That's what we've seen in past recoveries too. It's just that we've got a lot more long-term employed now."

But Fed Chair Janet Yellen has argued the opposite, when it comes to long-term unemployment. Two research papers out last month from the central bank stated the problem should normalize toward pre-recession levels as the recovery continues.

The minutes from the Fed's two-day policy-making meeting last month are scheduled for release Wednesday afternoon. While that gathering took place before last week's stronger employment report, investors will be looking for any hints on whether central bankers were starting to consider a path toward raising interest rates.

Rosenberg thinks the Fed should start increasing rates in early 2015, but acknowledges the consensus sees it more likely at the end of next year or early 2016.

"The bond market after June's FOMC meeting and the statement … [was] very convinced that it's going to be low for longer," he explained to "Squawk Box."

But he warned that could be changing: "There's a very low hurdle for that surprise because bond market yields are so low in the front end of the curve. So yes, I do think the market is going to be surprised."

As to whether so-called bond vigilantes will get tired of waiting for the Fed, Rosenberg said, "The bond markets can't overreact because they are waiting for a signal from the Fed."

"The issue," he continued, "is will you ever get a signal from the Fed. That's what people are concerned about in the [June] minutes. I don't think you'll see it this time around. But in July, it'll be more interesting."

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